US7620736B2 - Network topology having nodes interconnected by extended diagonal links - Google Patents
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Definitions
- the invention relates to computers and data communication networks.
- the invention has particular application in networks for carrying communications between processors of multi-processor computers.
- High performance computers are used to perform complex calculations. Such computers are typically used to run applications which perform extremely large numbers of calculations and/or process very large data sets. A high performance computer is required where a common computer cannot complete the required calculations in a practical interval. For example, a 7-day weather forecast is not useful if it takes 8 days of calculation to generate.
- high performance computers can be made faster by one or both of two basic design strategies: use faster CPU(s) or use more CPUs. Because of the relatively small market for high performance computers it is generally not cost effective to design and build unusually fast CPUs for use in high performance computers. Designing and testing a CPU is a very expensive undertaking that can typically be justified only if there are prospects for selling large quantities of the CPU. Further, device physics limitations make dramatic advances in CPU performance difficult to achieve.
- FIG. 1 shows a computer system 10 comprising a number of compute sub-systems 11 connected to a shared communication network 14 .
- Each compute sub-system 11 comprises a CPU 12 and memory 13 .
- each compute sub-system 11 comprises more than one CPU 12 that share memory 13 .
- Such computer sub-systems are referred to as Symmetric Multi-Processor (SMP) systems.
- FIG. 2 illustrates a computer system 10 A wherein, two or more compute sub-systems 11 are packaged in separate chassis 20 .
- high performance computers typically have mass storage to hold data.
- mass storage such as disk storage
- Network 14 plays a significant role in the performance of a computer system as shown in FIG. 1 or 2 .
- Network 14 may provide both internal communication (i.e. communication between compute sub-systems 11 ) and external communication (i.e. communication between a compute sub-system 11 and some computer or device external to computer system 10 ) or separate networks may be provided for internal and external communications.
- LAN local area network
- WAN wide area network
- Internal communication might be administrative in nature, or it might represent communication internal to a high performance computing application. Administrative communication has no special requirements, so LAN technology would be an appropriate solution for this type of communication. The internal communication of a high performance computing application requires further consideration.
- High performance computing applications are designed to split up a large complex problem into a multiplicity of smaller sub-problems that can be allocated to the available compute sub-systems 11 . Some of these applications are considered to be “embarrassingly parallel”, because each sub-problem can be solved independently. Little or no communication is required between the instances of application software solving the various sub-problems. Image rendering of computer-generated movie frames is one example of an “embarrassingly parallel” application, because each frame can be rendered independently. Such applications place no special requirements on shared communication network 14 . Cluster computers (a sub-category of high performance computers) with TCP/IP over Ethernet networks are often used to solve “embarrassingly parallel” problems.
- the topology of the communication network 14 in a high performance computer may provide multiple paths between any given source and destination.
- Communication network 14 may be configurable to support load balancing message traffic across the multiple paths.
- the bandwidth of network 14 may be characterized by a metric called the minimum bi-section bandwidth.
- a bi-section of a network is a division of the network into two halves, each containing half of the compute sub-systems 11 .
- the bi-section bandwidth is the aggregate bandwidth of all the data links that cross the bi-section. If we allow the bi-section to be arbitrarily placed, the minimum bi-section bandwidth arises for the bi-section with the smallest bi-section bandwidth.
- Communication latency is the time it takes to send a message between any two CPUs.
- Communication latency has two components: the inherent latency of the communication network 14 when no other message traffic is present, and the additional delays incurred by the presence of other message traffic.
- the inherent latency of communication network 14 depends upon factors including: the topology of network 14 (i.e. the number of switches and data links that must be traversed between sender and receiver), the latency to transmit a message from the sender, the latency to pass a message from one end of a data link to the other, the latency to pass a message through intervening switches, and the latency to accept a message at the receiver.
- the performance of applications which solve problems iteratively can be limited by maximum latency.
- the above stellar motion simulation might require processors to exchange stellar positions and velocities with other processors at the end of each simulated 1000 year interval. It is most convenient to exchange stellar position data after the position of each star has been calculated as of the end of the interval currently being considered.
- the evolution of the Milky Way may be simulated by determining stellar positions for each of a succession of 5 ⁇ 10 6 discrete times separated by 1000 year intervals.
- any single CPU may need to receive stellar position data from the other 9,999 CPUs before it can start the calculations for the next interval.
- the CPU is forced to wait to receive the last to come of the stellar position data from the other CPUs.
- the delay in receiving the last data is due to two factors: the time taken by the responsible CPU to calculate the last data and the time taken to communicate that data to the other CPUs. This constraint on performance is difficult to avoid when an application computes iteratively with communication between iterations. Many high performance computing applications exhibit this behavior.
- the topology of communication network 14 has a major impact on communication latency.
- the topology determines the number of data links and switches that a message has to pass through between a particular sender and a particular receiver.
- the number of hops to get through the communication network 14 acts as a multiplier on individual data link and switch latencies in calculating the overall latency.
- the topology of communication network 14 also has a secondary impact on bandwidth.
- the bandwidth of individual data links is a primary influence, but the topology also has an influence by providing multiple paths between senders and receivers. Data can be transmitted more quickly if it can be split between multiple paths.
- MIN multistage interconnect network
- hypercube (generally known as k-ary n-cube);
- toroid also generally known as k-ary n-cube
- FIG. 3 shows a computer system 30 having nodes 31 interconnected by a network 14 configured as a fat tree.
- Network 14 is represented as an upside down tree with nodes 31 at the leaves, data links 32 as the branches, and switches 33 where the branches join.
- a topmost switch 34 is the root of the tree.
- Fat trees were designed originally for use in networks implemented inside VLSI chips. In such networks a fat tree can be implemented using variable bandwidth data links.
- Each switch 33 has a single data link connected to its top side.
- the bandwidth of the top side data link is at least the sum of the bandwidths of the data links connected to the bottom side of the switch.
- the aggregate bandwidth of all data links is the same as at all other levels. As one goes up the tree, the bandwidth of individual data links increases.
- Switches at each level are duplicated and additional data links are added. All of the data links can have the same bandwidth. The aggregate bandwidth at each level of the tree still remains the same as at any other level of the tree.
- the duplication of switches has the side effect that there is the same number of switches at each level.
- FIG. 5 shows another example of a fat tree network. Eight port switches are used in a three level fat tree to connect 64 nodes together. All data links have the same bandwidth.
- a single layer fat tree can be constructed that connects together up to SP/2 nodes.
- a two layer fat tree can be constructed that connects together up to (SP/2) 2 nodes.
- a fat tree network with L layers can connect together up to (SP/2) L nodes.
- a fat tree network constructed to connect together N nodes must have at
- the maximum latency occurs in a fat tree network when a packet must travel all the way to a switch 34 at the top of the fat tree before it can descend to the destination node. This requires the packet to pass through every layer twice except for the top layer. The maximum latency for a fat tree network is thus
- the minimum bi-section bandwidth of a fat tree occurs for the bi-section which separates the fat tree into a left half and a right half. If there are N nodes connected by a fat tree network, and each is connected to the network by a single data link, the minimum bi-section bandwidth is (N/2) ⁇ linkBW, where linkBW is the bandwidth of each link.
- FIG. 6 shows a 6 ⁇ 7 2-dimensional mesh network 60 in which nodes 61 are interconnected by data links 62 . Each node 61 is connected to its nearest-neighbor nodes.
- mesh networks are usually designed with equal length sides in order to minimize the maximum latency.
- a toroid network is a mesh network that includes supplementary wrap-around data links connecting corresponding nodes on opposite sides of the topology.
- FIG. 7 shows a 6 ⁇ 6 2-dimensional toroid network 70 .
- FIG. 8 shows a 2 ⁇ 2 ⁇ 2 3-dimensional toroid network 80 .
- the nodes 81 A and 81 B that are directly opposite each other on opposite sides of the network are joined together by a wrap-around data link 82 . This is done for all possible directly opposite pairs of nodes.
- a toroid constructed from a mesh having D dimensions with sides each having length n can be used to connect together n D nodes.
- the individual nodes in a mesh or toroid network can be referenced by assigning them a coordinate based on a Cartesian coordinate system. If the mesh or toroid has D dimensions, each node can be assigned a coordinate with D components. For example a Cartesian coordinate system based on x, y, and z components can uniquely identify each node of a mesh or toroid having 3 dimensions. In this disclosure, numbering starts at 1 for each dimension. If the mesh or toroid has equal length n in each dimension then the numbering of each dimension ranges from 1 to n.
- the relative positions of two nodes in a mesh or toroid can be expressed as differences between the coordinates of the two nodes in each dimension.
- ⁇ x 1 , ⁇ x 2 , and ⁇ x 3 can refer to the differences in position in the three dimensions respectively.
- the data links of a mesh or toroid network can be referred to as Cartesian data links, because they follow the grid lines of a Cartesian coordinate system to which the nodes are mapped.
- a Cartesian data link connects two nodes whose coordinates are different in only one of the D dimensions.
- a toroid is a switchless communication network. Nodes are connected directly to one another. This requires that each node have a minimum of 2 ⁇ D ports to which data links can be connected.
- the maximum latency of a mesh network is D ⁇ (n ⁇ 1) or
- the maximum latency also occurs on the diagonals but the maximum latency is approximately half that of a similar mesh network, because the wrap-around data links provide a second alternative path for reaching the destination.
- the minimum bi-section bandwidth for a toroidal network is experienced when a toroid is bisected into a left half and a right half. If only one data link connects adjacent nodes, the minimum bi-section bandwidth is 2 ⁇ n D-1 ⁇ linkBW. The factor of 2 is due to the wrap-around data links.
- FIG. 9 plots maximum latency for both fat trees and toroidal networks as a function of the size of the number of nodes in a computing system. Latency is measured as the number of hops. In both networks the traversal of a data link is considered to be a hop. The maximum latency of a fat tree network depends on both the size of the computing system and the size of the switches being used in terms of switch ports. Curve 93 is for a fat tree constructed using switches each having 8 ports. Curve 94 is for a fat tree constructed using switches having 32 ports.
- the maximum latency of a toroid network depends on both the size of the computing system and the number of dimensions of the toroid. Curves 90 , 91 and 92 are respectively for toroids having 2, 3 and 4 dimensions. It can be seen that toroids generally have a higher maximum latency than fat tree networks. Maximum latency can only be reduced in a toroid network by using more dimensions. If enough dimensions are used, the maximum latency of a toroid network can be reduced to levels similar to a fat tree. Unfortunately the use of additional dimensions does not really help in practice, because many applications map most naturally to a toroid with 3 dimensions.
- FIG. 10 plots minimum bi-section bandwidth as a function of the number of nodes in a computing system.
- Bandwidth is measured as the number of data links crossing the bi-section.
- the number of data links can be converted to an actual bandwidth in bits per second by multiplying the number of data links by the bandwidth in bits per second of each data link.
- the minimum bi-section bandwidth of a fat tree only depends on the size of the computing system.
- Curve 100 shows the minimum bi-section bandwidth for a fat tree.
- the minimum bi-section bandwidth of a toroid network depends on both the size of the computing system and the number of dimensions of the toroid.
- Curves 101 , 102 and 103 are respectively for toroids having 4, 3 and 2 dimensions.
- a fat tree generally provides superior performance relative to a toroid in terms of lower maximum latency and greater minimum bi-section bandwidth.
- toroidal network topologies are used frequently because many applications model physical phenomena in a 3-dimensional continuum. In such applications, a majority of data communications is between nearest-neighbor nodes. In a toroid, nearest-neighbor nodes are always directly connected. Such applications, which may be called nearest-neighbor applications map well to toroidal topologies.
- nearest-neighbor applications do not map conveniently to fat tree networks.
- Nearest-neighbor applications typically treat a number of points arranged in a D-dimensional space. The points interact primarily with their nearest-neighbors. Such applications typically map each of the points to a node associated with a processor or group of processors so that calculations affecting the different points may be carried on in parallel. It is impossible to map a large number of points onto nodes without crossing a boundary in the fat tree network that forces network traffic to rise upwards to higher layers of the fat tree. For example, in FIG. 5 it is impossible to allocate a nearest-neighbor application to more than 32 nodes without some of the nodes being on opposite sides of the central divide 50 .
- the invention provides networks that are useful for interconnecting processors or other nodes in high-performance computer systems as well as for other data transmission applications.
- One aspect of the invention provides a network comprising a plurality of nodes interconnected in a regular D-dimensional array by Cartesian links. D is an integer and D ⁇ 2.
- the network also comprises a spatially regular arrangement of diagonal data links. For at least some of the diagonal links, in at least one dimension, the two nodes connected by the diagonal link are separated by a distance ⁇ x ⁇ 2.
- a shortest path between the two corresponding interconnected nodes by way of Cartesian links which link adjacent nodes is at least D+1 of such Cartesian links.
- each of the nodes in the network is connected by at least one of the diagonal data links to at least one other node in the network.
- the diagonal links may extend uniformly from each of the nodes.
- the diagonal links may comprise iso-delta diagonal links.
- the network may have sets of diagonal links with the links of each set having a different length.
- the diagonal links within each set may extend uniformly as described below.
- the diagonal links are iso-delta diagonal links as described below.
- the iso-delta diagonal links may include links having lengths of 2 P units, for two or more values of P where P is an integer.
- the nodes are arranged in a regular D-dimensional array of super-nodes.
- Each of the super-nodes comprises a plurality of the nodes.
- the diagonal links extend uniformly from each of the super-nodes but do not extend uniformly from at least some nodes of the super-nodes.
- FIG. 1 is a block diagram of a prior art high performance computer system
- FIG. 2 is a block diagram of a prior art high performance computer system having multiple chassis each accommodating multiple compute subsystems;
- FIG. 3 is a block diagram of a prior art fat tree network topology
- FIG. 4 is a block diagram of a prior art multiprocessor computer system having a fat tree topology implemented with a number of identical switches;
- FIG. 5 is a block diagram of a prior art 64 node computer system having a fat tree topology implemented with a number of identical switches;
- FIG. 6 is a block diagram of a prior art multiprocessor computer system having a 2 dimensional grid topology
- FIG. 7 is a block diagram of a prior art multiprocessor computer system having a 2 dimensional toroid topology
- FIG. 8 is a block diagram of a prior art multiprocessor computer system having a 3 dimensional toroid topology
- FIG. 9 is a plot of maximum latency as a function of size for computer systems having various topologies.
- FIG. 10 is a plot of minimum bi-section bandwidth as a function of size for computer systems having various topologies
- FIG. 11 is a diagram illustrating an iso-delta diagonal link in a computer system having a 2 dimensional grid topology
- FIG. 12 is a diagram of a 2-dimensional toroidal network which illustrates that a longer diagonal link can be replaced by a shorter diagonal link;
- FIG. 13A is a block diagram of a 2-dimensional mesh network having diagonal links according to a simple embodiment of the invention.
- FIG. 13B is a block diagram of a 2-dimensional mesh network having iso-delta diagonal links according to another simple embodiment of the invention.
- FIG. 14 is a block diagram of a 2-dimensional toroidal network having uniformly extending diagonal links
- FIG. 15 is a block diagram illustrating the effect of diagonal links on bi-section bandwidth
- FIG. 16 is a block diagram of a 2-dimensional toroidal network having nodes linked both by Cartesian links and by iso-delta diagonal links of length 3 ;
- FIG. 17 is a block diagram of a 2-dimensional toroidal network having nodes linked both by Cartesian links and by iso-delta diagonal links of lengths 1 and 2 ;
- FIG. 18 is a schematic diagram showing iso-delta diagonal and Cartesian links connecting to a particular node of a three-dimensional toroidal network according to an embodiment of the invention.
- FIG. 19 is a block diagram of a network according to an embodiment of the invention wherein some links pass through switches.
- FIG. 20 is a block diagram of a network according to an embodiment of the invention wherein nodes are clustered into super-nodes and the super-nodes are interconnected by diagonal links.
- This invention relates to communication networks capable of providing data communications between a number of nodes.
- the networks of the invention are particularly applicable to providing communications between processors or groups of processors in a multi-processor computer system.
- the term node is used herein to describe a point to which a communication network can deliver or receive data.
- a node may be, for example, a CPU, a group of CPUs, a group of compute sub-systems which share a connection to the communication network, a switch, one or more processors interconnected with one or more switches, or the like.
- each node is on a different physical module, such as a chassis which is separate from the chassis on which other nodes are located.
- a network according to the invention has an array of nodes arranged in a grid topology.
- each node can be mapped to a point in a Cartesian coordinate system of D dimensions where D is two, three, or more.
- Grid topologies include meshes and toroids of two or more dimensions.
- the grid includes links which wrap around to provide a toroid topology.
- the nodes are interconnected by a regular pattern of diagonal links.
- the two nodes connected by the diagonal link are separated by a distance ⁇ x ⁇ 2. If the nodes have insufficient ports to support the desired number of Cartesian and diagonal data links, the invention provides for the provision of switches in a regular pattern.
- Each node is connected to the nearest switch (“nearest” means topologically nearest and does not refer to the physical location of a device which performs the switching).
- Diagonal and/or Cartesian data links interconnect the switches. Some embodiments provide diagonal links of two or more different lengths.
- the same pattern of diagonal data links extend from every node.
- Diagonal links of different lengths may originate at each node.
- the diagonal links extend uniformly from each node.
- the diagonal links may include “iso-delta” diagonal links which meet the “iso-delta” constraint
- ⁇ x may be used as a unit of length for iso-delta diagonal links. It would be necessary to traverse one unit of length in every dimension by way of Cartesian links to reach the same node that one could reach by traversing one unit of length on an iso-delta diagonal.
- each node 111 of toroid 110 is marked with its Cartesian coordinates x 1 , x 2 .
- the latency to reach each node 111 from node 111 A by way of Cartesian links 112 is written beneath each node.
- Starting at node 111 A which has coordinate (2, 2) the maximum latency of 6 is experienced trying to reach node 111 B with coordinates (5, 5) as indicated by arrow 113 .
- Nodes located relative to node 111 A on other diagonals, that do not meet the iso-delta constraint can be reached in fewer Cartesian hops because fewer units of length have to be traversed on at least one of the dimensions to reach such nodes.
- Diagonal data links provided in embodiments of this invention may wrap around a toroidal network in the same manner as Cartesian data links. Where this occurs, it is not necessary to provide diagonal data links longer than half the maximum diagonal distance across the toroid, because such a long data link can always be replaced with a shorter data link that travels in roughly the opposite direction and wraps around the toroid.
- FIG. 12 shows a diagonal link 120 joining nodes 111 A and 111 C.
- Link 120 is equivalent to the shorter diagonal link 121 .
- This invention provides networks having regular diagonal links in addition to Cartesian links. The most benefit per diagonal link is achieved by adding diagonal data links connecting nodes such that the iso-delta constraint is satisfied. Less benefit is achieved by adding diagonal data links connecting nodes that do not meet the iso-delta constraint.
- FIG. 13A shows a network 130 A according to a simple embodiment of the invention.
- Network 130 A has a number of nodes 132 arranged in a 2-dimensional mesh and interconnected by Cartesian links 134 extending along the coordinate directions in the mesh.
- Nodes 132 are also interconnected by diagonal links 136 A and 136 B (collectively links 136 ).
- links 136 are not iso-delta diagonal.
- Each diagonal link 136 provides bi-directional data communication between two nodes which are three hops apart by way of Cartesian links 134 .
- Network 130 A can be modified by adding wrap-around Cartesian links in one or both dimensions to provide an underlying toroidal topology. Additional links 136 which wrap around may also be provided whether or not the Cartesian links provide a toroidal topology.
- FIG. 13B shows a network 130 B according to another simple embodiment of the invention wherein nodes 132 are connected by iso-delta diagonal links 137 of length two.
- the links to node (4,3) are emphasized.
- Node (4,3) has Cartesian links connecting it to each of nodes (4,4), (5,3), (4,2) and (3,3).
- Node (4,3) has iso-delta diagonal links connecting it to each of nodes (6,5) (6,1), (2,1) and (2,5).
- Diagonal links 137 wrap around (e.g. diagonal link 137 A connects nodes (5,2) and (1,6)).
- FIG. 14 shows diagonal links 142 for all possible combinations of ⁇ 1 and 1 for ⁇ x 1 and ⁇ 2 and 2 for ⁇ x 2 as well as all possible combinations of ⁇ 2 and 2 for ⁇ x 1 and ⁇ 1 and 1 for ⁇ x 2 .
- Diagonal links 142 can be provided for every node 143 . For clarity, diagonal links are shown in FIG. 14 only for one node 143 A.
- links 142 of FIG. 14 can be viewed as a specification for the other links 142 .
- link 142 A has values of 2 and 1 for ⁇ x 1 and ⁇ x 2 respectively. These values can be called “specifying values”.
- the specifying values can be manipulated to generate the component deltas for the remaining data links. Two different manipulations are used. The first manipulation takes all combinations of positive and negative values. Since there are D specifying values, one for each dimension and each specifying value can be used to generate a link extending in either the positive or the negative direction in a particular dimension, there are 2 D such combinations of positive and negative values.
- the second manipulation uses every possible permutation of allocating one of the specifying values to each of ⁇ x 1 and ⁇ x 2 . If there are D specifying values, there are D! ways of allocating these values to ⁇ x 1 , ⁇ x 2 , . . . , ⁇ x D . In combination, these two manipulations generate 2 D ⁇ D! different diagonal data links where the specifying values are all different. If some of the specifying values are the same then the number of unique diagonal data links is given by:
- links D ! ⁇ 2 D ⁇ k ⁇ ( dup k ! ) ( 1 )
- links is the number of unique diagonal links
- the specifying values include k duplicated values
- dup k is the number of duplicates for the k th one of the k duplicated values.
- iso-delta diagonal data links to every node.
- a toroid of D dimensions there are 2 D possible directions in which iso-delta diagonal data links can extend from any node.
- In a 3-dimensional network there are 8 possible directions in which iso-delta diagonal data links can be sent.
- In a 4-dimensional network there are 16 possible directions in which such data links can be sent, and so on.
- iso-delta diagonal data links of length 1 these possible directions result from all the possible combinations of the values ⁇ 1 and +1 for all ⁇ x i where 1 ⁇ i ⁇ D.
- iso-delta diagonal data links extend from each node in all possible directions.
- Diagonal data links and especially iso-delta diagonal data links, increase the minimum bi-section bandwidth of a toroid. Like the Cartesian data links, they do this by crossing the bi-section.
- a Cartesian data link is inefficient at increasing minimum bi-section bandwidth.
- Each Cartesian data link is oriented along a single dimension (i.e. for a Cartesian data link ⁇ x i ⁇ 0 for only a single dimension i).
- a Cartesian data link can only contribute to bi-section bandwidth when the dimension along which it is oriented is cut by the bi-section.
- diagonal data links are defined such that ⁇ x i ⁇ 0 for multiple dimensions.
- Diagonal data links can contribute to bi-sections of all dimensions for which ⁇ x i ⁇ 0.
- Iso-delta diagonal data links can contribute to bi-sections of all dimensions.
- iso-delta diagonal link 151 in the 2-dimensional 6 ⁇ 6 toroidal network 150 of FIG. 15 Because ⁇ x i ⁇ 0 for both the x 1 and x 2 dimensions, diagonal data link 151 contributes to bandwidth across both of bi-sections 152 and 153 .
- FIG. 16 shows a 2-dimensional 6 ⁇ 6 toroid network 160 having iso-delta diagonal data links each three units in length (i.e.
- 3) extending to and from all of its nodes. It can be seen that all of the iso-delta diagonal data links cross the bi-section 163 somewhere along their length. Since each node terminates 4 iso-delta diagonal data links, and each such data link is connected to two nodes, there are 2N iso-delta diagonal data links crossing bi-section 163 . The minimum bi-section bandwidth is
- linkBW ( 2 ⁇ N + 2 ⁇ N D - 1 D ) ⁇ linkBW which is significantly greater than the minimum bi-section bandwidth of an equivalent fat tree network which is given by N/2 ⁇ linkBW.
- the diagonal data links may all have the same length, or they may have different lengths.
- the minimum bi-section bandwidth and maximum latency of a network will depend in part on the quantity and lengths of the diagonal data links. By adjusting the quantity and lengths of the diagonal data links, any desired minimum bi-section bandwidth within reason can be achieved.
- the diagonal data links should be of multiple lengths in order to provide lowest-latency access to diverse regions of the network.
- preferred embodiments of the invention use iso-delta diagonal data links of various lengths. It is also beneficial to combine the use of diagonal data links of various lengths with the use of Cartesian data links of various lengths. Empirical evidence suggests that judicious choice of data links can reduce maximum latency to a level that is comparable to the maximum latency of a fat tree network interconnecting an equal number of nodes.
- FIG. 17 shows a 2-dimensional 6 ⁇ 6 toroidal network 170 in which iso-delta diagonal data links 172 A and 172 B (collectively links 172 ) respectively defined by
- 1 and
- 2 for all dimensions extend uniformly from each node.
- 6 diagonal data links 172 cross bi-section 176 for every Cartesian data link 174 that crosses bi-section 176 .
- Bi-section bandwidth is 7 times what it would be if there were no diagonal data links.
- latencies to reach each node starting from node (2,2) are written under each node. It can be seen by comparing FIG. 17 to FIG. 11 that maximum latency is reduced from 6 hops to 3 hops. For comparison, a fat tree interconnecting 36 nodes using 16 port switches would have a maximum latency of 4 hops.
- Node 182 has coordinates (1, 4, 6).
- Iso-delta diagonal links of lengths 1 , 2 and 4 are provided.
- Some embodiments of the invention include switches arranged in a regular pattern.
- each node may be connected to one or more switches.
- Diagonal and/or Cartesian data links interconnect the switches.
- Such embodiments of the invention can use nodes having insufficient ports to support the desired number of Cartesian and diagonal data links. In some cases, nodes may even have insufficient ports to connect nodes together with Cartesian data links.
- Switches provide a convenient way of expanding the effective port count of nodes. The cost of adding switches is that extra hops are incurred. This can increase latency. Any suitable packet forwarding device, such as a router, can be used in place of a switch.
- FIG. 19 shows an example network 190 which includes nodes 191 and switches 192 .
- Switches 192 reduce the number of ports used at each node 191 .
- Nodes 191 are each connected to 4 adjacent switches 192 by links 193 .
- Switches 192 are interconnected by iso-delta diagonal links 194 defined by
- 1 and
- 2 where ⁇ x i is measured relative only to other switches.
- Nodes 191 are interconnected in a grid topology by Cartesian links 195 . There is one switch 192 for every node 191 . Switches 192 can be conceptually paired with nodes 191 .
- Each pair 197 of a switch and a node 191 including the link 193 connecting the switch and node can be considered to be itself a node. Pairs 197 are connected by Cartesian links 195 and diagonal links 194 .
- each node 191 requires only 8 ports to which data links can be connected.
- Each switch 192 connects to 8 other switches. Without switches 192 , each node 191 would require 12 ports to handle 8 iso-delta diagonal data links and 4 Cartesian data links. Switches 192 may optionally be additionally interconnected with other switches 192 by way of Cartesian links (not shown).
- adjacent nodes are grouped into super nodes which each contain a number of nodes.
- Each super-node is connected to other super nodes by diagonal links.
- Such embodiments can be implemented with nodes which have a reduced number of ports since it is not necessary to provide a full range of diagonal links to every node.
- the nodes in each super-node may be arranged in a hypercube.
- a hypercube having D dimensions and sides which each have a length that is a multiple of 2.
- Adjacent nodes in the toroid can be grouped into D-dimensional hypercubes. In two dimensions a hypercube is a square, while in three dimensions a hypercube is a cube. If each side of the toroid has the same length n, the number of hypercubes that can be formed is (n/2) D .
- Each hypercube has 2 D nodes. Each of these nodes is at a corner of the hypercube. Diagonal data links can be used to connect the corners of the super-nodes (hypercubes) together. As noted above, there are 2 D different directions in which iso-delta diagonal data links can be sent from a node in D-dimensional toroid. By aggregating nodes into super-nodes, it is only necessary to send iso-delta diagonal data links in one direction from any one node rather than 2 D directions. In a network which uses iso-delta diagonal data links, this reduces the number of ports that a node is required to have by a factor of 2 D . The port requirement is also reduced for non-iso-delta diagonal data links.
- FIG. 20 shows a 2-dimensional 8 ⁇ 8 toroidal network 200 .
- Dashed lines show the grouping of adjacent nodes 202 into super-nodes (hypercubes) 204 .
- the Cartesian links 203 interconnecting the nodes of each super-node are supplemented with diagonal data links 205 which can reduce latency within each super-node 204 .
- Super-nodes 204 are interconnected by iso-delta diagonal data links 207 A and 207 B defined respectively by
- 1 and
- 2 where ⁇ x i is measured relative to super-nodes 204 . If all of nodes 202 were interconnected by iso-delta diagonal data links, each node 202 would be required to have 12 ports. In the network of FIG. 20 , each node is only required to have 7 ports.
- this invention may be applied to provide communication networks which combine the advantages of both toroid networks and fat tree networks.
- Such networks can provide the low latency and communication relationships of a toroid network for nearest-neighbor type applications.
- the network For non-nearest-neighbor applications with other communication patterns (e.g. all-to-all, one-to-all, all-to-one communication patterns), the network provides a small maximum latency and large minimum bi-section bandwidth equal to or superior to that of a fat tree network capable of handling the same number of nodes.
- each of the links may be provided by a physical layer comprising one or more wires, optical fibers or other signal conductors. Data may be carried on such a physical layer according to any suitable protocol.
- the links may comprise InfiniBandTM, Ethernet, Gigabit Ethernet or 10 Gigabit Ethernet links, OC-12 or OC-48 links, SONET, ATM links and so on.
- routing logic (which may include or consist of static routing tables) is associated with the nodes and/or switches in a network according to the invention so that data can be routed efficiently between nodes.
- the routing logic may include load balancing logic which may direct data in parallel along different paths connecting the same endpoints in the network.
- a component e.g. a link, node, processor, assembly, device, circuit, etc.
- reference to that component should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e., that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the invention.
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Abstract
Description
hops.
hops.
where links is the number of unique diagonal links, the specifying values include k duplicated values, and dupk is the number of duplicates for the kth one of the k duplicated values. Iso-delta diagonal links are a special case where all of the specifying values are the same so that equation (1) reduces to links=2D.
which is significantly greater than the minimum bi-section bandwidth of an equivalent fat tree network which is given by N/2×linkBW.
-
- While it is typically convenient to make meshes and toroids usually with equal-length sides in order to minimize the maximum latency, this is not required. The invention may also be applied to topologies based upon meshes and toroids with sides of non-equal lengths in different dimensions.
- While the invention has been described in terms of high performance computer systems, it is equally applicable to any communication network based on the mesh or toroid topology.
Accordingly, the scope of the invention is to be construed in accordance with the substance defined by the following claims.
Claims (20)
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GB0417549D0 (en) | 2004-09-08 |
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US20050044195A1 (en) | 2005-02-24 |
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